Three‐dimensional effects in shear waves

Abstract

Most studies on shear waves to date have assumed the flow is depth uniform (two dimensional). In the present study, we utilize the quasi‐three‐dimensional (quasi‐3D) nearshore circulation model SHORECIRC to study shear waves. Our results show that shear wave flow is more organized in the quasi‐3D simulation than in the 2D simulation. In the 2D simulation, the vortices are moving farther offshore of the bar, while in the quasi‐3D simulation, they are more confined to the shoreward side of the bar. Moreover, the shear waves in the quasi‐3D simulation are much less energetic than in the 2D simulation, though the total momentum mixing for the two cases is not significantly different. To understand which mechanisms cause the differences in the 2D and the quasi‐3D simulation, the momentum, kinetic energy, and enstrophy equations for the mean flow and the shear waves are derived. The momentum, energy, and enstrophy balances are discussed using the numerical results from the idealized SUPERDUCK topography and the wave conditions on October 16, 1986. The effects of the quasi‐3D dispersion due to the depth varying currents on shear waves are illustrated. Analysis of the mean momentum balance shows that both the shear waves and the quasi‐3D current pattern contribute to the momentum transfer, and the momentum transfer provided by the shear waves is sometimes larger than that by the quasi‐3D dispersive terms. The kinetic energy balance of the shear waves shows that the quasi‐3D dispersive terms will extract kinetic energy from the depth‐averaged shear waves. Furthermore, the enstrophy equation demonstrates that the quasi‐3D dispersion terms provide vortex tilting, which allows three‐dimensional vortex interactions.